4
Example 2
• What is the z
What is the z
score for the value of 95 in the
score for the value of 95 in the
following
values?
following
values?
X = [96, 114, 100, 97, 101, 102, 99, 95, 90]
( )
2
X
X
M
X
M
M
SD
Z
N
N
SD


=
=
=
∑
∑
5
Example 2 Answers
•
X
= [
96
114
100
97
101
102
99
95
90
96
114
100
97
101
102
99
95
90], so the mean of X, M =
99.33 (M =
∑
X/ N = 894/9).
•
(X  M) = [3.33, 14.67, 0.67, 2.33, 1.67, 2.67, 0.33, 4.33, 9.33]
• Deviation score, subtract M from each number in
X.
•
(X – M)
2
= [11.09, 215.21, 0.45, 5.43, 2.79, 7.13, 0.11, 18.75, 87.05]
• Squared deviations from the mean, M.
•
SS=
Σ
(X  M
)
2
=
348.01
• Sum of squared deviations from the mean (SS).
•
SD
2
= SS / N = 38.67
• Average squared deviation from the mean.
•
SD=
√
SD
2
= 6.22
• Square root of variance.
6
Example 2 Answers
• First compute the mean and standard deviation.
First compute the mean and standard deviation.
These values are respectively 99.33 & 6.22.
These values are respectively 99.33 & 6.22.
• ZScore
Score
= (95
= (95
–99.33)/6.22
99.33)/6.22
=
0.70
0.70
.
• Thus, the data value of 95 is located 0.70
Thus, the data value of 95 is located 0.70
standard deviation
standard deviation
below
below
the mean value of
the mean value of
99.33 (since the z
99.33 (since the z
score is negative).
score is negative).